PRE-CALCULUS
ENGG 10
(1 unit Lec; 2 units Lab)
CHAPTER I. ALGEBRA
A. The Set of Real Numbers
1. Integer Exponents
2. Polynomials, Operations, Special Products
3. Binomial Expansion (Binomial Theorem)
4. Factoring Polynomials
B. Rational Expressions
1. Rules of Exponents; Simplification of Rational Expressions; Operations on Rational Expressions
2. Properties of Radicals; Simplification of Radicals
3. Operations on Radicals
4. Complex Numbers
C. Equations in One variable
1. Linear Equations; Literal Equations
2. Quadratic Equations in One Variable
3. Word Problems
4. Other Equations in One Variable: Radical, Fractional, Quadratic in Form
5. Polynomial Equation of Degree n
D. Functions
1. Inverse Functions
2. Exponential and Logarithmic Functions
3. Exponential and Logarithmic Equations
E. Systems of Linear Equations
1. Elimination Method
2. Substitution Method
F. Decomposition of Rational Expressions into Partial Fractions
G. Inequalities
1. Linear, Quadratic, and Polynomial Inequality
2. Linear Inequalities with Absolute Value
CHAPTER II. TRIGONOMETRY
A. Trigonometric Functions
1. Angles and Measurement
2. Trigonometric Functions of Angles
3. Trigonometric Function Values
4. The Sine and Cosine of Real Numbers
5. Graphs of the Sine and Cosine and Other Sine Waves
6. Solutions of Right Triangle
B. Analytic Trigonometry
1. The Eight Fundamental Identities
2. Proving Trigonometric Identities
3. Sum and Difference Identities
4. Double-Measure and Half-Angle Identities
5. Inverse Trigonometric Functions
6. Trigonometric Equations
7. Identities for the Product, Sum, and Difference of Sine and Cosine
CHAPTER III. ANALYTIC GEOMETRY
A. Plane Analytic Geometry
1. The Cartesian Planes
2. Distance Formula
3. Point-of-Division Formulas
4. Inclination and Slope
5. Parallel and perpendicular Lines
6. Angle from One Line to Another
7. An Equation of a Locus
B. The Line
1. Point-Slope and Two-Point Forms
2. Slope-Intercept and Intercept Forms
3. Distance from a Point to a Line
4. Normal Form
C. The Circle
1. The Standard Form for an Equation of a Circle
2. Conditions to Determine a Circle
D. Conic Sections
1. Introduction
2. The Parabola
3. The Ellipse
4. The Hyperbola
E. Curve Tracing in two-dimensional space
1. Rectangular form
2. Polar form
CHAPTER IV. SOLID MENSURATION
A. Plane Figures
1. Mensuration of Plane Figures
B. Solids for which V = Bh
1. Solid Sections
2. Cubes
3. Rectangular Parallelopiped
4. Cavalieri’s Theorem
5. Volume Theorem
6. Prism
7. Cylindrical Surface
8. Cylinder (Circular and Right Circular)
C. Solids for which V = (1/3) Bh
1. Pyramids
2. Similar Figures
3. Cones
4. Frustum of Regular Pyramid
5. Frustum of Right Circular Cone
D. Sphere
1. Surface Area and Volume
2. Zone
3. Segment
4. Sector
E. Theorems of Pappus
References
1. Leithold, Louis. College Algebra and Trigonometry. Massachusetts: Addison-Wesley.
2. Mijares, Catalina. College Algebra.
3. Swokowski, Earl W. and Jeffrey A. Cole Algebra and Trigonometry with Analytic Geometry, 10th ed ed.
Brooks/ Cole Publishing Co., 2001.
4. Feliciano and Uy, Modern Trigonometry
5. Kern, Willis F. and Bland James R. Solid Mensuration with Proofs 2nd ed. John Wiley &Sons, Inc.
6. Sigley, Daniel T. and Stratton, William T. Solid Geometry and Mensuration.Dryden Press
7. Dugopolski, Mark. College Algebra, 3rd ed. Addison-Wesley, 2002.
GRADING SYSTEM:
Course Components Weight
LECTURE Midterm Examination 15%
Final Examination 15%
Major Outputs 70%
Passing Rate: 50%
